Question 188758
Solve by completing the square:
{{{5x^2-x-2 = 0}}} To complete the square, you need to have the {{{x^2}}} coefficient = 1, so divide through by 5.
{{{(5x^2-x-2)/5 = 0}}} Simplify.
{{{(1/5)x^2-(1/5)x-2/5 = 0}}} Now add {{{2/5}}} to both sides.
{{{(1/5)x^2-(1/5)x = 2/5}}} Complete the square in x by adding the square of half the x-coefficient {{{(1/10)^2 = 1/100}}} to both sides.
{{{(1/5)x^2-(1/5)x+1/100 = 2/5 + 1/100}}} Factor the left side and simplify the right side.
{{{(x-1/10)^2 = 41/100}}} Now take the square root of both sides.
{{{x-1/10 = (sqrt(41))/10}}} or {{{x-1/10 = -(sqrt(41))/10}}} Add {{{1/10}}} to both sides of each of these.
{{{x = 1/10+-sqrt(41)/10}}}
{{{highlight(x = 1/10 +(sqrt(41))/10)}}} or {{{highlight(x = 1/10 - (sqrt(41))/10)}}}